5.1 THE BASIC DEFINITION

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À  p

The acceleration of a point `P' is the first derivative of velocity, or second derivative of position,

To analyze linear acceleration we must first separate the velocity into a magnitude, and direction.

We can also consider angular acceleration,

If we consider the relative velocity and acceleration between two points on a rigid body we get,

For planar calculations we can write a complex equivalent,

As an example, let's consider the four bar mechanism below,

there are a couple of other relationships of use,

Apparent acceleration is found by first separating velocity into magnitude and direction.

Note: the coriolis component above happens in systems with moving frames of reference. This can create a whip effect.

Consider the example below,

Apparent Angular acceleration is found using,

For rolling contact the centripetal and normal accelerations are zero, therefore we can simplify the apparent acceleration equation to,

Consider the example below,

We can also solve these problems using simple derivatives. Consider the example below,

Consider the accelerations of the joints in the four bar linkage below,